Problem: Divide the polynomials.
Usually, there are many different ways to divide polynomials. Here, we will use the method of splitting the quotient into multiple quotients: $\dfrac{x^4+2x^2-5}{x}=\dfrac{x^4}{x}+\dfrac{2x^2}{x}-\dfrac{5}{x}$ Now let's try to cancel common factors in the resulting terms. $\begin{aligned} \dfrac{x^4}{x}&=x^3 \\\\ \dfrac{2x^2}{x}&=2x \end{aligned}$ $-\dfrac{5}{x}$ doesn't have common factors so it has to stay as it is. In conclusion, this is the result of dividing the polynomials: $x^3+2x-\dfrac{5}{x}$ [I want to see a different way of performing the division.]